Scientific Notation, Significant Figures Notes Chapter 1 Some Basic Concepts of Chemistry Chemistry Class 11 NCERT

Scientific notation
It is exponential notation in which any number can be represented in the form N × 10ⁿ where n is an exponent having positive or negative values and N can vary between 1 to 10.
Example
we can write 232.508 as 2.32508 x 10² in scientific notation.
Teach addition , subtraction, multiplication and division of exponential notations

Significant Figures
(1) Zeros at the end or right of a number are significant provided they are on the right side of the decimal point. Otherwise, the zeros are not significant.  For example, 0.200 g has three significant figures. But100 has only one significant figure.
(2)  Zeros preceding to first non-zero digit are not significant. Such zero indicates the position of decimal point.
Example:
0.03  has  one significant figure
0.0052 has two significant figures.

(3) When numbers are written in scientific notation, the number of digits between 1 and 10 gives the number of significant figures
Examples:
4.01×10²     has three significant figures,
8.256 × 10^–3          has four significant figures.
(4)Zeros between two non-zero digits are significant. Thus, 2.005 has four significant figures.

Addition and Subtraction of Significant Figures
The result cannot have more digits to the right of the decimal point than either of the original numbers.

Here, 18.0 has only one digit after the decimal point and the result should be reported only up to one digit after the decimal point which is 31.1.

Multiplication and Division of Significant Figures
In these operations, the result must be reported with no more significant figures as are there in the measurement with the few significant figures.
2.5×1.25 = 3.125
Since 2.5 has two significant figures, the result should not have more than two significant figures.
Rounding off the numbers
· If the rightmost digit to be removed is more than 5, the preceding number is increased by one. for example 1.386 If we have to remove 6, we have to round it to 1.39
· If the rightmost digit to be removed is less than 5, the preceding number is not changed. For example, 4.334 if 4 is to be removed, then the result is rounded upto 4.33.
· If the rightmost digit to be removed is 5, then the preceding number is not changed if it is an even number but it is increased by one if it is an odd number. For example, if 6.35 is to be rounded by removing 5, we have to increase 3 to 4 giving 6.4 as the result. However, if 6.25 is to be rounded off it is rounded off to 6.2.
Dimensional Analysis
Often while calculating, there is a need to convert units from one system to other. The method used to accomplish this is called factor label method or unit factor method or dimensional analysis.